Probability Distributions: Standard distributions such as normal, gamma, beta, Weibull, multinomial, Poisson, multivariate normal; sampling distributions of statistics such as t,F,chi-squared and T² ( central and non-central) distributions, order statistics; limit theorems.

Estimation: Confidence intervals; mean squared error. UMV unbiased estimates; maximum likelihood estimates; Cramer-Rao inequality; sufficiency and completeness; Rao-Blackwell and Lehmann-Scheffe theorems; notions of Bayesian and sequential estimation; applications to problems involving standard distributions.

Hypotheses Testing: MP, UMP, and UMP unbiased tests; likelihood ratio tests; power of a test; efficiency of a test; notions of Bayesian and sequential tests; applications to problems involving standard distributions.

Nonparametric Inference: Categorical data; Chi square tests; Wilcoxon one-sample and two-sample tests: Kolmogorov-Smirnov tests; permutation tests.

Linear Models: Correlation and multiple regression; least squares; Gauss-Markov theorem; Cochran's theorems; coefficients of partial determination; analysis of variance in one-way and two-way layouts, randomized block design.

Most of the material above can be found in

1. Introduction to Mathematical Statistics by R. Hogg and A. Craig
2. Statistical Theory by B. Lindgren
3. Mathematical Statistics: basic ideas and selected topics by P.J. Bickel and K.A. Doksum
4. Mathematical Statistics and Data Analysis by John Rice
5. Linear Statistical Inference and Its Applications by C.R. Rao